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Proof step 4 from proof middle-coef-max_exp (previous step)

i ^ i0 ≤ 2 * j, 2 * j < i ^ (i0 + 1), i | binom_coef(2 * j, j), prime(i), 2 * j < i ^ max_exp(i, binom_coef(2 * j, j)), 0 < j, 0 ≤ i0, i ^ i0 < i ^ (i0 + 1), i ^ i0 < i ^ max_exp(i, binom_coef(2 * j, j)) ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 5:
max_exp(i, binom_coef(2 * j, j)) ≤ i0, i ^ i0 ≤ 2 * j, 2 * j < i ^ (i0 + 1), i | binom_coef(2 * j, j), prime(i), 2 * j < i ^ max_exp(i, binom_coef(2 * j, j)), 0 < j, 0 ≤ i0, i ^ i0 < i ^ (i0 + 1), i ^ i0 < i ^ max_exp(i, binom_coef(2 * j, j)) ⊦
Proof step 7:
i ^ i0 ≤ 2 * j, 2 * j < i ^ (i0 + 1), i | binom_coef(2 * j, j), prime(i), 2 * j < i ^ max_exp(i, binom_coef(2 * j, j)), 0 < j, 0 ≤ i0, i ^ i0 < i ^ (i0 + 1), i ^ i0 < i ^ max_exp(i, binom_coef(2 * j, j)) ⊦ max_exp(i, binom_coef(2 * j, j)) ≤ i0

Rule argument

fma: max_exp(i, binom_coef(2 * j, j)) ≤ i0

Additional information

Used formulas: max_exp(i, binom_coef(2 * j, j)) ≤ i0